A261081 a(n) = number of steps required to reach 0 from F(n+2)-1 by repeatedly subtracting from a natural number the number of ones in its Zeckendorf representation. Here F(n) = the n-th Fibonacci number, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, ...

0, 1, 2, 3, 5, 7, 10, 15, 23, 34, 51, 76, 113, 169, 254, 384, 583, 888, 1357, 2080, 3198, 4931, 7624, 11817, 18356, 28567, 44529, 69503, 108606, 169868, 265898, 416506, 652844, 1023945, 1607063, 2524041, 3967245, 6240679, 9825201, 15481987, 24416683, 38539839, 60880089

Offset

0,3

Links

Table of n, a(n) for n=0..42.

Formula

a(n) = A219642(A000045(n+2)-1).

a(0) = 0; for n >= 1, a(n) = A261091(n) + a(n-1).

Other identities. For all n >= 0:

a(n) = A261082(n)-1.

Prog

(Scheme, two alternatives, the other one using memoizing definec-macro)
(define (A261081 n) (A219642 (- (A000045 (+ 2 n)) 1)))
(definec (A261081 n) (if (zero? n) n (+ (A261091 n) (A261081 (- n 1)))))

Crossrefs

One less than A261082.

Partial sums of A261091.

Cf. A000045, A219642, A261102.

Sequence in context: A003410 A362757 A018133 * A116975 A286227 A134792

Adjacent sequences: A261078 A261079 A261080 * A261082 A261083 A261084

Keyword

nonn

Author

Antti Karttunen, Aug 08 2015

Status

approved